To share stuff between characters, you just have to put those equipments into your town chest. This chest is linked and shared between all your characters on the same season, meaning Legacy or Chronicles. You can not share stuff between one Legacy char and one Chronicles char.
Speaking of that, here is the explanation:
-Chronicles are based on seasons and Chronicle mode is the "current" version of the game, including all the latest changes, gameplay, quest, items, etc. Actually it's only Chronicle 1, meaning we don't really know how it's gonna work for the next one, but it will always be "Chronicle mode = last season of the game". You always need to create a new char to play the new Chronicle.
-Legacy is the "old" version of the game, including all Chronicles but the last one. Since it's only Chronicle 1 atm, "Legacy" only mean the first version of the game without all those dragon quests and the tracking beast thing. We can suppose that when Chronicle 2 will be out, the Chronicle 1 will join Legacy and our old chars will be able to complete tracks, dragon quest, etc.